The article identifies nullification with anti-slavery efforts before the Civil War. Calhoun isn't mentioned at all in this historical article about nullification, anti-slavery, and the Confederacy which is an interesting omission. Confederate leaders are alleged to be against nullification as stated in this quote from the article:

As we can see, Davis framed nullification as a principle that was malicious. Alexander Stephens, who would become the Vice President of the Confederacy, expressed similar views when considering nullification 1858, saying that he “did not believe in the doctrine of nullification.” Stephens firmly categorized himself as “no nullifier” during a debate about South Carolina’s usage of nullification during the Andrew Jackson administration. It is clear that both individuals not only despised nullification, but also considered it unconstitutional.

I am not going to untangle these historical claims about Jefferson Davis and his legal thinking or claims about nullification in the 19th century.

What is really interesting is that the Tenth Amendment Center is wanting to make it clear that they aren't neo-Confederate and they don't want people to identify nullification with the Confederacy.